Time Space Complexity Research Articles

Exactly solvable non-unitary time evolution in quantum critical systems I: effect of complex spacetime metrics

Abstract In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal (2021 arXiv:2105.10161) and Witten (2021 arXiv:2111.06514) on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including the entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibit universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

On complexity of colloid cellular automata

The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from them. We analyze the space-time complexity of Boolean circuits derived from the electrical responses of colloids-specifically ZnO (zinc oxide, an inorganic compound also known as calamine or zinc white, which naturally occurs as the mineral zincite), proteinoids (microspheres and crystals of thermal abiotic proteins), and their combinations in response to electrical stimulation. To extract Boolean circuits from colloids, we send all possible configurations of two-, four-, and eight-bit binary strings, encoded as electrical potential values, to the colloids, record their responses, and infer the Boolean functions they implement. We map the discovered functions onto the cell-state transition rules of cellular automata-arrays of binary state machines that update their states synchronously according to the same rule-creating the colloid cellular automata. We then analyze the phenomenology of the space-time configurations of the automata and evaluate their complexity using measures such as compressibility, Shannon entropy, Simpson diversity, and expressivity. A hierarchy of phenomenological and measurable space-time complexity is constructed.

Comments on the Derivation of Formulas for Gaussian Quasiphotons by Complex Space-Time Ray Methods (STRM)

Comments on the Derivation of Formulas for Gaussian Quasiphotons by Complex Space-Time Ray Methods (STRM)

Understanding the Spatial Narratives of Puzzle Films Using Cognitive Maps

Spatial narratives are becoming increasingly significant in contextualizing geographical phenomena. Whereas many studies focus on spatial narratives of real spaces projected from the Earth’s surface, this article examines the imaginary spaces in the narrative of Hollywood puzzle films, arguing that cognitive maps are more effective in understanding and navigating these spaces. Through an analysis of well-known puzzle films, the article demonstrates how cognitive maps can encode imaginary spaces, draw the audience’s attention to key landmarks, and guide both the filmmaker and the audience through the film’s narrative. Beyond films, this study underscores the potential of cognitive maps in decoding complex space–time relationships in real-world context. By bridging the gap between cinematic imagination and geographical exploration, this article aims not only to inspire filmmakers but also to encourage geographers, cartographers, and GIScientists to look beyond their own fields and draw inspiration from other areas, such as cinematography, to envision a terra incognita that extends beyond the real world.

PRINCIPLES OF ORGANIZATION OF THE MATERIAL WORLD

An attempt has been made to present and describe the PRINCIPLES OF ORGANIZATION OF THE MATERIAL WORLD using the “Scheme of the structure of our world”, which is the foundation of the philosophy of Hermeticism. In it, the three parts of the philosophy of the Universe are designated as the three Kingdoms that make up our world - Abstractions, Mass and Gravity, as well as Radiation. A diagram is shown for converting time into mass and back to implement phase transitions of matter into various states in the series: radiation – free space – dark matter – baryonic matter – black holes. The Scheme points to the location of dark energy. The geometric body of the rank space and the fractal principle of its construction are demonstrated. The previously proposed concepts were repeated: a) material zero as an elementary/electromagnetic quantum of space EQS; b) space-time complex of STC inside the quantum of space; c) the axis of the speed of time as an indicator for phase transitions of space quanta.

Cosmic inflation epochs and Complex space time wormhole solutions.

Cosmic inflation epochs and Complex space time wormhole solutions.

1920년대 조선야소교서회의 교양서적 번역이 기행문학에 미친 영향

This paper examines the trends and meanings of translation and publication of cultural books by the JoseonYasogyoseohoi(The Christian Literature Society of Korea) during the Japanese colonial period, and Ann Judson Sajeok(Ann Judson), Yurakhwangdogi(The Swiss Family Robinson) and GeurusoPhyorugi(Robinson Crusoe), which are adventure stories for missionary purposes. The goal is to identify the internal structure of and its influence on the development of travel literature. 
 As a personal biography of a great man, Ann Judson and the drift novels Yurakhwangdogi and GeurusoPhyorugi, although their genres are different, have something in common in terms of travel experience, drifting, and cross-cultural contact. This means that these works contributed greatly to the development of Korean travel literature, but there are certain differences in the internal structure of the works depending on the differences in genre. Due to the nature of biographies of great people, Ann Judson has a relatively simple narrative structure in which the flow of time and movement through space are relatively simple. In comparison, other two drifted novels are works that appropriately embody the motif of ‘travel → drifting → settlement → return’, and are works that appropriately reproduce the chronotope as a space-time complex at the level of travel literature. In particular, the illustrations used in Geuruso are pictures that specifically express the time and space signified within the text, and become noteworthy elements in relation to the restructuring of space and time in travel literature. In this way, adventure stories for missionary purposes can be said to be important works in terms of the development of travel literature, even if Bible translations remain or cultural prejudices based on civilizational discourse are inherent.

T-violation and the dark sector

It is argued, as a working hypothesis, that “normal” and dark matter interactions can only be [Formula: see text]- and [Formula: see text]-violating. One way to implement this idea is to consider that time reversal in dark matter is implemented, not by an antiunitary operator, but by an unitary operator. It is shown how this occurs naturally in the context of complex spacetime with an extended symmetry group.

Lifting query complexity to time-space complexity for two-way finite automata

Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not been used to study time-space tradeoffs of finite automata. We design a new technique showing that separations of query complexity can be lifted, via communication complexity, to separations of time-space complexity of two-way finite automata. As an application, one of our main results exhibits the first example of a language L such that the time-space complexity of two-way probabilistic finite automata with a bounded error (2PFA) is Ω˜(n2), while of exact two-way quantum finite automata with classical states (2QCFA) is O˜(n5/3), that is, we demonstrate for the first time that exact quantum computing has an advantage in time-space complexity comparing to classical computing.

Gravitation from optimized computation: Einstein and beyond

A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the linearized level, in holographic theories with Einstein gravity duals, assuming the so-called ‘Complexity-Volume’ (CV) proposal. We expand on this proof in two significant directions. First, we derive higher-derivative gravitational equations by including appropriate corrections to the CV dictionary. Second, we show semi-classical equations arise by considering the leading bulk quantum corrections to CV. Our proof is valid for two-dimensional dilaton gravities, where the problem of semi-classical backreaction can be solved exactly. However, we argue the principle should hold more generally, leading us to a concrete proposal for bulk complexity of perturbative excited states in arbitrary dimensions. Our results demonstrate the robustness of spacetime complexity as a guiding principle to understand gravity in terms of quantum computation.

Holomorphic general coordinate invariant modified measure gravitational theory

Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in real space time. In this context here spacetime is extended to complex spacetime and standard general coordinate invariance is also extended to complex holomorphic general coordinate transformations. This is possible by introducing a non Riemannian Measure of integration, which transforms avoiding non holomorphic behavior. Instead the measure transforms according to the inverse of the jacobian of the coordinate transformation and avoids the traditional square root of the determinant of the metric −g. which is not globally holomorphic, or the determinant of the vierbein which is sensitive to the vierbein orientations and not invariant under local lorentz transformations with negative determinants. A contribution to the cosmological term appears as an integration constant in the equations of motion. A proposed action for Finsler geometry, which involves −g rather than −g will also constitute an example of a Holomorphic General Coordinate Invariant Modified Measure Gravitational Theory.

Solitons and dynamics for the shifted reverse space–time complex modified Korteweg–de Vries equation

Solitons and dynamics for the shifted reverse space–time complex modified Korteweg–de Vries equation

A Product Fuzzy Convolutional Network for Detecting Driving Fatigue.

Existing driving fatigue detection methods rarely consider how to effectively fuse the advantages of the electroencephalogram (EEG) and electrocardiogram (ECG) signals to enhance detection performance under noise conditions. To address the issues, this article proposes a new type of the deep learning (DL) framework based on EEG and ECG called the product fuzzy convolutional network (PFCN). It should be noted that this article first investigates how to fuse EEG and ECG signals to deal with driving fatigue detection under noise conditions in both simulated and real-field driving environments. Specifically, the PFCN includes three subnetworks. The first uses a fuzzy neural network (FNN) with feedback and a product layer, effectively capturing the particularity and temporal variation of high-dimensional EEG signals and reducing the time-space complexity. The second subnetwork uses a 1-D convolution to convert the ECG data into feature sequences, providing high accuracy and low computational complexity in ECG data classification. The third subnetwork proposes a fusion-separation mechanism to effectively fuse the extracted ECG and EEG features, suppressing the noise interference and ensuring higher detection accuracy. To evaluate the performance of PFCN, a series of experiments has been set up in both simulated and real-field driving environments. The results indicate that the proposed PFCN model has better robustness and detection accuracy compared with several mainstream fatigue detection models.

"In Search of an Integrated Corona Knowledge Ecosystem for Actionable Health Policy – A Mind Mapping Voyage and an Exploratory Decomposition in Spatial Pandemetrics"

"This paper seeks to map out the knowledge re quirements and infrastructure needed for a com prehensive and quantitative analysis of the societal and geographical dimensions of effective policies regarding COVID-19 (‘coronametrics’ or ‘pandemet rics’). After a sketch of limitations and challenges in corona research, a multi-layer mind map is designed in order to systematically scan the cognitive needs in the corona domain and to address both health policy and socioeconomic-medical information requirements in a geographic context, with a par ticular view to the use of actionable dashboards. A systematic decomposition of the corona knowledge system is pursued to acquire a coherent insight into gaps in corona knowledge, with particular emphasis on policy and research relevance. It turns out that the study of causality patterns in the complex space time evolution of COVID-19 is the Achilles’ heel in the analysis of pandemetrics and calls for new effective and preventive research"

Features extraction for traffic sign recognition

Traffic sign recognition (TSR) is the basic technology of the Advanced Driving Assistance System(ADAS) and intelligent automobile, while a highly qualified feature vector plays a key role in TSR. Therefore, the feature extraction of TSR has become active research in the fields of computer vision and intelligent automobiles. Although deep learning features have made a breakthrough in image classification, it is difficult to apply to TSR because of its large scale of training dataset and high space-time complexity of model training. Considering visual characteristics of traffic signs and external factors such as weather, light, and blur in real scenes, an efficient method to extract high-qualified image features is proposed. As a result, the lower-dimension feature can accurately depict the visual feature of TSR due to its powerful descriptive and discriminative ability. In addition, benefiting from a simple feature extraction method and lower time cost, our method is suitable to recognize traffic signs online in real-world applications scenarios. Extensive quantitative experimental results demonstrate the effectiveness and efficiency of our method.

Switching clusters’ synchronization for discrete space-time complex dynamical networks via boundary feedback controls

Unlike the existing literatures that consider only discrete-time networks, this paper explores the double effects of both discrete time and discrete spatial diffusions in a switching complex dynamical networks. By means of the knowledge of clusters controls, a clusters synchronous frame of space-time discrete switching complex networks with boundary feedback controller is newly proposed and established. With the helps of some indispensable vector-valued sequence inequalities and Lyapunov function with switching signals and clusters’ information, the boundary feedback controllers are designed to synchronize space-time discrete switching complex networks coupled with nodes’ states or spatial diffusions in the form of clusters. Additionally, a realizable computer algorithm is given to make the derived results of this paper easier to enforce. The current work is pioneering in consideration of discrete spatial diffusions and provides a theoretical and practical basis for future research in this regard.

Efficient shallow learning as an alternative to deep learning

The realization of complex classification tasks requires training of deep learning (DL) architectures consisting of tens or even hundreds of convolutional and fully connected hidden layers, which is far from the reality of the human brain. According to the DL rationale, the first convolutional layer reveals localized patterns in the input and large-scale patterns in the following layers, until it reliably characterizes a class of inputs. Here, we demonstrate that with a fixed ratio between the depths of the first and second convolutional layers, the error rates of the generalized shallow LeNet architecture, consisting of only five layers, decay as a power law with the number of filters in the first convolutional layer. The extrapolation of this power law indicates that the generalized LeNet can achieve small error rates that were previously obtained for the CIFAR-10 database using DL architectures. A power law with a similar exponent also characterizes the generalized VGG-16 architecture. However, this results in a significantly increased number of operations required to achieve a given error rate with respect to LeNet. This power law phenomenon governs various generalized LeNet and VGG-16 architectures, hinting at its universal behavior and suggesting a quantitative hierarchical time–space complexity among machine learning architectures. Additionally, the conservation law along the convolutional layers, which is the square-root of their size times their depth, is found to asymptotically minimize error rates. The efficient shallow learning that is demonstrated in this study calls for further quantitative examination using various databases and architectures and its accelerated implementation using future dedicated hardware developments.

The Impact of High-Speed Rail on Economic Development: A County-Level Analysis

High-speed rail has an important impact on the location choices of enterprises and the labor force, which is reflected in a complex space–time process. Previous studies have been unable to show the change characteristics between enterprises and the labor force at the county level. Therefore, based on the new economic geography theory, we first constructed a theoretical analysis framework to explore high-speed railway’s impact on county economy development and then obtained the two economic subdivision factors’ impacts: industrial enterprises and secondary labor force. Then, based on the panel data of 1791 county units in China from 2003 to 2019, the study constructed a multi-period PSM-DID model to empirically explore high-speed rail’s impact on the county’s agglomeration of industrial enterprises and secondary labor force. The results show that high-speed rail has a long-term negative effect on the county area’s agglomeration of industrial enterprises. From the perspective of the labor force, high-speed rail has a long-term and continuous positive effect on the agglomeration of the secondary labor force in county units.

A Dynamic Spatio-Temporal Stochastic Modeling Approach of Emergency Calls in an Urban Context

Emergency calls are defined by an ever-expanding utilisation of information and sensing technology, leading to extensive volumes of spatio-temporal high-resolution data. The spatial and temporal character of the emergency calls is leveraged by authorities to allocate resources and infrastructure for an effective response, to identify high-risk event areas, and to develop contingency strategies. In this context, the spatio-temporal analysis of emergency calls is crucial to understanding and mitigating distress situations. However, modelling and predicting crime-related emergency calls remain challenging due to their heterogeneous and dynamic nature with complex underlying processes. In this context, we propose a modelling strategy that accounts for the intrinsic complex space–time dynamics of some crime data on cities by handling complex advection, diffusion, relocation, and volatility processes. This study presents a predictive framework capable of assimilating data and providing confidence estimates on the predictions. By analysing the dynamics of the weekly number of emergency calls in Valencia, Spain, for ten years (2010–2020), we aim to understand and forecast the spatio-temporal behaviour of emergency calls in an urban environment. We include putative geographical variables, as well as distances to relevant city landmarks, into the spatio-temporal point process modelling framework to measure the effect deterministic components exert on the intensity of emergency calls in Valencia. Our results show how landmarks attract or repel offenders and act as proxies to identify areas with high or low emergency calls. We are also able to estimate the weekly average growth and decay in space and time of the emergency calls. Our proposal is intended to guide mitigation strategies and policy.

Augmented AI-Knowledge Driven Intelligent Systems for Adversarial-Dynamic Uncertainty & Complexity: Designing Self Adaptive Complex Systems for Quantum Uncertainty and Time Space Complexity

Augmented AI-Knowledge Driven Intelligent Systems for Adversarial-Dynamic Uncertainty & Complexity: Designing Self Adaptive Complex Systems for Quantum Uncertainty and Time Space Complexity